Genotype-covariate correlation and interaction disentangled by a whole-genome multivariate reaction norm model

The genomics era has brought useful tools to dissect the genetic architecture of complex traits. We propose a reaction norm model (RNM) to tackle genotype-environment correlation and interaction problems in the context of genome-wide association analyses of complex traits. In our approach, an environmental risk factor affecting the trait of interest can be modeled as dependent on a continuous covariate that is itself regulated by genetic as well as environmental factors. Our multivariate RNM approach allows the joint modelling of the relation between the genotype (G) and the covariate (C), so that both their correlation (association) and interaction (effect modification) can be estimated. Hence we jointly estimate genotype-covariate correlation and interaction (GCCI). We demonstrate using simulation that the proposed multivariate RNM performs better than the current state-of-the-art methods that ignore G-C correlation. We apply the method to data from the UK Biobank (N= 66,281) in analysis of body mass index using smoking quantity as a covariate. We find a highly significant G-C correlation, but a negligible G-C interaction. In contrast, when a conventional G-C interaction analysis is applied (i.e., G-C correlation is not included in the model), highly significant G-C interaction estimates are found. It is also notable that we find a significant heterogeneity in the estimated residual variances across different covariate levels probably due to residual-covariate interaction. Using simulation we also show that the residual variances estimated by genomic restricted maximum likelihood (GREML) or linkage disequilibrium score regression (LDSC) can be inflated in the presence of interactions, implying that the currently reported SNP-heritability estimates from these methods should be interpreted with caution. We conclude that it is essential to correctly account for both interaction and correlation in complex trait analyses and that the failure to do so may lead to substantial biases in inferences relating to genetic architecture of complex traits, including estimated SNP-heritability.